Bipartite Matching: Graph Theory and the Ford-Fulkerson Algorithm

Finding optimal pairings—whether matching jobs to applicants, tasks to servers, or roommates to apartments—is a fundamental challenge in computer science. Bipartite graphs and network flow algorithms provide a robust mathematical framework to solve these allocation problems efficiently. In this text-only course, you will transition from understanding basic graph theory to confidently implementing and tracing the Ford-Fulkerson algorithm to find maximum matchings. You will learn how to structure bipartite matching problems as flow networks and verify your solutions step-by-step. What you'll learn: - Understand the core concepts of bipartite graphs, independent sets, and matching theory. - Convert bipartite matching problems into standard network flow networks with source and sink vertices. - Apply the Ford-Fulkerson algorithm and the augmenting path concept to find maximum matchings. - Trace execution steps manually to verify the correctness of your matching solutions. - Analyze the time complexity and efficiency of matching algorithms in real-world scenarios. - Explore modern applications of matching algorithms in resource allocation, scheduling, and market design. You will start with foundational graph terminology and definitions before moving into the mechanics of flow networks. Through clear written explanations and step-by-step code walkthroughs, you will master the conversion process and algorithm execution. This course is designed for aspiring software engineers, computer science students, and algorithm enthusiasts who want to strengthen their discrete mathematics and problem-solving skills. No prior experience with network flow is required. Start reading today to master one of the most elegant and practical algorithms in computer science.